Upper bound and lower bound

  • Thread starter l46kok
  • Start date
  • #1
l46kok
297
0

Homework Statement



1.
f(n) = n - 100
g(n) = n - 200

2.
f(n) = log(2n)
g(n) = log(3n)

n >= 0 in all cases
Find out if f(n) is an upperbound, lowerbound or both of g(n)

Homework Equations





The Attempt at a Solution



in case of 1, f(n) has to be an upperbound of g(n) because when graphed together, f(n) has to be an upperbound of g(n).

For 2, solution does not exist at n = 0. Otherwise, f(n) is a lower bound of g(n). Does this mean that f(n) is a lower bound or both?
 

Answers and Replies

  • #2
HallsofIvy
Science Advisor
Homework Helper
43,021
970

Homework Statement



1.
f(n) = n - 100
g(n) = n - 200

2.
f(n) = log(2n)
g(n) = log(3n)

n >= 0 in all cases
Find out if f(n) is an upperbound, lowerbound or both of g(n)

Homework Equations





The Attempt at a Solution



in case of 1, f(n) has to be an upperbound of g(n) because when graphed together, f(n) has to be an upperbound of g(n).
Too vague. What you should say is "200> 100 so -100> -200 and n- 100> n- 200 for all n. Since f(n)> g(n) for all n, f is an upper bound of g."

For 2, solution does not exist at n = 0. Otherwise, f(n) is a lower bound of g(n). Does this mean that f(n) is a lower bound or both?
Is suspect that should not be "[itex]n\ge 0[/itex] for both cases" but only n> 0 for the second. As you point out, ln(0) is not defined so the problem makes no sense for n= 0.

ln(2)< ln(3) so ln(n)+ ln(2)< ln(n)+ ln(3) for all n> 0. ln(2n)< ln(3n) for all n> 0.
 

Suggested for: Upper bound and lower bound

  • Last Post
Replies
16
Views
397
  • Last Post
Replies
3
Views
635
Replies
9
Views
529
Replies
11
Views
446
Replies
2
Views
1K
Replies
1
Views
685
Replies
11
Views
543
Replies
3
Views
864
Replies
7
Views
415
Replies
5
Views
207
Top